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Open Access Highly Accessed Methodology article

EM algorithm for Bayesian estimation of genomic breeding values

Takeshi Hayashi1* and Hiroyoshi Iwata2

Author Affiliations

1 Division of Animal Sciences, National Institute of Agrobiological Sciences, Kannondai, Tsukuba, Ibaraki 305-8602, Japan

2 Data Mining and Grid Research Team, National Agricultural Research Center, Kannondai, Tsukuba, Ibaraki 305-8666, Japan

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BMC Genetics 2010, 11:3  doi:10.1186/1471-2156-11-3

Published: 22 January 2010

Abstract

Background

In genomic selection, a model for prediction of genome-wide breeding value (GBV) is constructed by estimating a large number of SNP effects that are included in a model. Two Bayesian methods based on MCMC algorithm, Bayesian shrinkage regression (BSR) method and stochastic search variable selection (SSVS) method, (which are called BayesA and BayesB, respectively, in some literatures), have been so far proposed for the estimation of SNP effects. However, much computational burden is imposed on the MCMC-based Bayesian methods. A method with both high computing efficiency and prediction accuracy is desired to be developed for practical use of genomic selection.

Results

EM algorithm applicable for BSR is described. Subsequently, we propose a new EM-based Bayesian method, called wBSR (weighted BSR), which is a modification of BSR incorporating a weight for each SNP according to the strength of its association to a trait. Simulation experiments show that the computational time is much reduced with wBSR based on EM algorithm and the accuracy in predicting GBV is improved by wBSR in comparison with BSR based on MCMC algorithm. However, the accuracy of predicted GBV with wBSR is inferior to that with SSVS based on MCMC algorithm which is currently considered to be a method of choice for genomic selection.

Conclusions

EM-based wBSR method proposed in this study is much advantageous over MCMC-based Bayesian methods in computational time and can predict GBV more accurately than MCMC-based BSR. Therefore, wBSR is considered a practical method for genomic selection with a large number of SNP markers.